R. Litherland. (2002)cite arxiv:math/0207099
Comment: 19 pages, 5 figures.
Zusammenfassung
Carter, Jelsovsky, Kamada, Langford and Saito have defined an invariant of
classical links associated to each element of the second cohomology of a finite
quandle. We study these invariants for Alexander quandles of the form
Zt,t^-1/(p, t^2 + kappa t + 1), where p is a prime number and t^2 + kappa t
+ 1 is irreducible modulo p. For each such quandle, there is an invariant with
values in the group ring ZC_p of a cyclic group of order p. We shall show
that the values of this invariant all have the form Gamma_p^r p^2s for a
fixed element Gamma_p of ZC_p and integers r >= 0 and s > 0. We also describe
some machine computations, which lead us to conjecture that the invariant is
determined by the Alexander module of the link. This conjecture is verified for
all torus and two-bridge knots.
%0 Generic
%1 Litherland2002a
%A Litherland, Richard A.
%D 2002
%K algebra homology knot-theory quandles
%T Quadratic quandles and their link invariants
%U http://arxiv.org/abs/math/0207099
%X Carter, Jelsovsky, Kamada, Langford and Saito have defined an invariant of
classical links associated to each element of the second cohomology of a finite
quandle. We study these invariants for Alexander quandles of the form
Zt,t^-1/(p, t^2 + kappa t + 1), where p is a prime number and t^2 + kappa t
+ 1 is irreducible modulo p. For each such quandle, there is an invariant with
values in the group ring ZC_p of a cyclic group of order p. We shall show
that the values of this invariant all have the form Gamma_p^r p^2s for a
fixed element Gamma_p of ZC_p and integers r >= 0 and s > 0. We also describe
some machine computations, which lead us to conjecture that the invariant is
determined by the Alexander module of the link. This conjecture is verified for
all torus and two-bridge knots.
@misc{Litherland2002a,
abstract = { Carter, Jelsovsky, Kamada, Langford and Saito have defined an invariant of
classical links associated to each element of the second cohomology of a finite
quandle. We study these invariants for Alexander quandles of the form
Z[t,t^{-1}]/(p, t^2 + kappa t + 1), where p is a prime number and t^2 + kappa t
+ 1 is irreducible modulo p. For each such quandle, there is an invariant with
values in the group ring Z[C_p] of a cyclic group of order p. We shall show
that the values of this invariant all have the form Gamma_p^r p^{2s} for a
fixed element Gamma_p of Z[C_p] and integers r >= 0 and s > 0. We also describe
some machine computations, which lead us to conjecture that the invariant is
determined by the Alexander module of the link. This conjecture is verified for
all torus and two-bridge knots.
},
added-at = {2009-05-22T16:31:26.000+0200},
author = {Litherland, Richard A.},
biburl = {https://www.bibsonomy.org/bibtex/22300263cb91bfedbeda50acf44abb24b/njj},
description = {Quadratic quandles and their link invariants},
interhash = {1e6df55e969ed3e636aba45f71202457},
intrahash = {2300263cb91bfedbeda50acf44abb24b},
keywords = {algebra homology knot-theory quandles},
note = {cite arxiv:math/0207099
Comment: 19 pages, 5 figures},
timestamp = {2009-05-22T16:31:26.000+0200},
title = {Quadratic quandles and their link invariants},
url = {http://arxiv.org/abs/math/0207099},
year = 2002
}